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%% lexture14.tex
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%% Made by Alex Nelson
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%% Started on  Sun Jun 20 12:44:46 2010 Alex Nelson
%% Last update Sun Jun 20 12:48:50 2010 Alex Nelson
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We have defined a reductive Lie algebra as the complexification
of the Lie algebra for a compact group. The Cartan subalgebra
(usually denoted $\mathfrak{h}$) corresponds to the maximal torus
in the group $T\subset G$ is the maximal, Abelian, connected
subgroup. Diagrammatically 
\begin{equation}
\begin{diagrams}
\mathfrak{g} & \rTo^{\exp} & G\\
\uTo         &             & \uTo\\
\mathfrak{h} & \rTo^{\exp} & T
\end{diagrams}
\end{equation}
